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The authors generalise the idea of \(LU\)-\(LU\)-operators for sequences, derive the analogies and define a \(LU\)-\(LU\)-structure for functions of a real variable. \(LU\)-\(LU\)-operators -- also known as MaxMin and MinMax filters -- are local, non-linear rank order filters which efficiently and successfully remove impulsive noise superposed on a sequence. The \(LU\)-\(LU\)-operators have very attractive mathematical properties compared to other non-linear filters. By applying sub operators \(L\) (low) and \(U\) (upper) positive and negative outliers can be removed. A successive application of the combination (\(LU\) or \(UL\)) results in a smoother sequence than the original one. The generalisation consists in that the lower and upper envelopes of functions can be associated with a pair of \(L\) and \(U\) operators and an \(LU\)-\(LU\)-structure can be defined. The \(LU\)-\(LU\)-structure maps a function onto the envelopes and thus, as in the case of sequences, reduces variations and smoothes the original function. Since the main resources of impulsive noise include the atmospheric impacts, industry generated noises, radar, mobile communication, computer networks, muscular noise, etc., it is possible to assume that the ideas of this article could be successfully applied to image processing, engineering, earth and medical sciences. Note: the reviewer found the following misprints: Page 91, line 5: \((L_nx)_i = \max\{\min\{x_{i-n},\dots, x_i\},\min\{x_{i-n+1},\dots, x_{i+1}\},\dots, \max\{x_i,\dots,x_{i+n}\}\} \rightarrow (L_nx)_i = \max\{\min\{x_{i-n},\dots, x_i\}, \min\{x_{i-n+1},\dots, x_{i+1}\},\dots, \min\{x_i,\dots, x_{i+n}\}\}\). Section 3, definition 3.1, (a), line 6: \dots if \(f\) is lower semicontinuous \(\dots \rightarrow \dots\) if \(f\) is upper semicontinuous \(\dots\) Section 3, definition 3.3, line 7: \(\dots {F},{G}; { M}[{ X}] \dots \rightarrow \dots { F},{ G}: { M}[{ X}]\dots\) Page 94, after multiplication table, lines 2, 4, 5: Lemma 1 \(\to\) Lemma 3.2.